Controlled-source electromagnetic (“CSEM”) surveys are becoming an important geophysical tool for evaluating the presence of hydrocarbon-bearing strata within the earth. CSEM surveys typically record the electromagnetic signal induced in the earth by a source (transmitter) and measured at one or more receivers. The behavior of this signal as a function of transmitter location, frequency, and separation (offset) between transmitter and receiver can be diagnostic of rock properties associated with the presence or absence of hydrocarbons. A notable diagnostic rock property of this kind is electrical resistivity. Thus, CSEM measurements are typically used to determine the spatially-varying resistivity of the subsurface.
In the marine environment, CSEM data are typically acquired by towing an electric dipole transmitting antenna 10 among a number of receivers 11 positioned on the seafloor 12 (FIG. 1). The receivers typically have multiple sensors designed to record different vector components of the electric and/or magnetic fields. The transmitter antenna is typically towed (by a vessel on the sea surface 13) a few tens of meters above the seafloor. The receivers are weighted and fall to the seafloor, but release their weight and rise back to the surface with the data after receiving an acoustic command from the ship. Alternative configurations include stationary transmitters on the seafloor or in the water column as well as magnetic transmitter antennae. The transmitting and receiving systems typically operate independently (without any connection between them), so that receiver data must synchronized with shipboard measurements of transmitter position by comparing clock times on the receivers to time from a shipboard or GPS (Global Positioning System) standard.
CSEM data are typically interpreted in the temporal frequency domain, each signal representing the response of the earth to electromagnetic energy at that temporal frequency. Temporal frequency domain means the data is transformed, typically by Fourier transformation, such that the dependence of the data on time becomes dependence on frequency. In raw data, the strength of each frequency component varies depending on how much energy the transmitter broadcasts (i.e., the amplitude of each component in the transmitter's frequency spectrum) and on the receiver sensitivity at that frequency. These transmitter and receiver effects are typically removed from the data prior to interpretation. FIGS. 2A-B depict raw receiver data 21 together with the transmitter waveform 22 that gave rise to it. FIG. 2A displays measured data on a time scale of several hours while FIG. 2B shows the received signal (and, for reference, the transmitted signal) on a much shorter time scale, comparable to the transmitter signal period, typically between 4 and 32 seconds. (The vertical scale applies only to the receiver signal.)
In practice, the receiver data are usually converted to temporal frequency by dividing (or “binning”) the recorded time-domain data into time intervals (x1, x2, and x3 in FIG. 3A) equal to the transmitter waveform period (FIG. 3A) and determining the spectrum within each bin by standard methods based on the Fourier transform (FIG. 3B). (The phases of the spectral components are not shown.) With each bin is associated a time, typically the Julian date at the center of the bin. Since the transmitter location is known as a function of time, these bins may be interchangeably labeled in several different ways: by Julian date of the bin center; by transmitter position; by the signed offset distance between source and receiver; or, by the cumulative distance traveled by the transmitter relative to some arbitrarily chosen starting point. In general, the received signals are made up of components both in-phase and out-of-phase with the transmitter signal. The signals are therefore conveniently represented as complex numbers in either rectangular (real-imaginary) or polar (amplitude-phase) form. The transmitter signal may be a more complex waveform than that depicted in FIGS. 2B and 3A.
Those skilled in the art of digital signal processing will know of techniques that will decompose time series, such as raw CSEM data, to temporal frequency without explicitly dividing the data into non-overlapping time intervals. In general, a time series may be transformed to the time-frequency domain and the dominant temporal frequencies extracted separately as functions of time. Some methods of transforming data to the time-frequency domain include the Short-Time Fourier Transform (J. Allen, L. Rabiner, “A Unified Approach to Short-Time Fourier Analysis and Synthesis,” Proc. of the IEEE 65, 1558-64, (1977)); the Wavelet Transform (W. C. Lang and K. Forinash, “Time-frequency analysis with the continuous wavelet transform,” Am. J. Phys. 66, 794-797, (1998)); the Wigner-Ville transform (E. Wigner, On the quantum correction for thermodynamic equilibrium, Phys. Rev. 40, 749-759, (1932), and J. Ville, “Theorie et application de la notion de signal analytique,” Cables et Transmission, 2A., 61-74, (1948)); the Choi-Williams transform (H. Choi and W. Williams, “Improved time-frequency representation of multicomponent signals using exponential kernels,” IEEE Trans. on Acoust., Speech, and Signal Processing, 37, 862-871, (1989)); and the Bessel method (Z. Guo, L. G. Durand, and H. C. Lee, “The time-frequency distributions of nonstationary signals based on a Bessel kernel,” IEEE Trans. on Signal Proc., 42, 1700-1707, (1994)). The present invention is not limited to any particular method or methods for spectral decomposition of CSEM data to the temporal frequency domain.
“Skin depth” is a useful concept in many applications of electromagnetism. For a material with conductivity σ given in (Ω-m)−1 the skin depth is given byδ=√{square root over (2/(ωμσ))}where ω is the angular frequency in rad/sec and μ≈4π×10′−7 H/m is the magnetic permeability. The skin depth is the distance over which a plane electromagnetic wave will decay in amplitude by a factor of e−1, where e is the base of the natural logarithmic system (Ward et al., “Electromagnetic Theory for Geophysical Applications,” page 138, in Electromagnetic Methods in Applied Geophysics, v. 1, Nabighian, ed., Society of Exploration Geophysics (1987)). This loss of amplitude corresponds to a transfer of energy into the material in the form of heat. With no risk of confusion, skin depth can be thought of either as a property of the material and how it responds to electromagnetic waves of different frequencies or as a characteristic of electromagnetic waves and how they propagate in different materials.
Marine CSEM survey data are strongly dependent on the skin depth in water. This dependence is twofold. First, the attenuation in water controls how much electromagnetic energy will be broadcast into the sediments beneath the water. In practical marine CSEM applications, this effect creates a preference for towing the transmitter close to the seafloor. Second, and more importantly for this invention, the attenuation controls how much electromagnetic energy will be broadcast into the air above the water. In particular, if the transmitter is several skin depths below the air-water boundary, the amplitudes broadcast into the air will be weakened by several factors of e. In addition, these signals propagating in the air will be weakened by additional factors of e as they penetrate the water in order to be captured by the receivers. Conversely, if the transmitter and receivers are within one skin depth of the air-water boundary, a significant portion of the measurement will correspond to signals propagating through the air.
Water conductivities typically depend on the amount and type of dissolved chemicals as well as on the temperature. For example, sea water might have conductivities in the range of 1-5 (Ω-m)−1 while potable lake water has conductivities in the range 0.005-0.05 (Ω-m)−1. FIG. 4 shows the dependence of skin depth on conductivity at four different frequencies, from top to bottom: 0.01, 0.1, 1, and 10 Hz. Thus, the skin depth at 1.0 Hz in seawater with conductivity 3.0 (Ω-m)1 is approximately 290 meters. In the ocean, water conductivities can vary, for example, at river mouths where fresh water mixes with more conductive salt water.
In the following, words such as “seawater”, “marine”, and “ocean” are used with the understanding that similar observations will apply for fresh water and lakes provided the differences in conductivity are taken into account.
The arrival (at a CSEM receiver) of significant electromagnetic energy through the air can overwhelm the effects of hydrocarbon reservoirs in CSEM data, making it difficult for the CSEM data interpreter to discern the presence or absence of hydrocarbon reservoirs in the subsurface. The source of the problem is twofold. Firstly, energy traveling through the air can be very strong since there is little attenuation of the electromagnetic waves in air (the skin depth is very long). Secondly, both air and hydrocarbon-bearing strata can give rise to similar features in CSEM data, since both materials are generally much more resistive than other earth strata. Since the earth's atmosphere is always present during CSEM data acquisition, all CSEM data will contain signals that arise because of the presence of the air. Such components of the CSEM signal may be referred to as “air waves” or “air-wave noise”. This definition of air-wave noise includes signals that arise because of refractions at the air-water interfaces and wave-guide effects in the water column as well as signals that literally follow paths through the air. In general, CSEM receivers record signals that have reflected one or more times within the air-water-sediment system. So, in addition to recording signals that have reflected from the air layer and signals that have reflected from the subsea sediments, the data will include signals that first reflected from the air and were subsequently reflected from subsea strata of interest before arriving at the receiver. While such multiply-reflected signals do contain some information about subsea strata, they are dominated by the reflection from the air layer and the electrical properties of air and are therefore considered noise in most CSEM surveys. As described above, air-wave noise is substantially decreased when the seawater is several skin depths thick, since the electromagnetic energy will be strongly attenuated as it travels to and from the air layer. Conversely, the level of air-wave noise increases as the water becomes more shallow, being particularly onerous when the water thickness is two skin depths or less.
FIGS. 5 and 6 serve to illustrate the impact of air-wave noise on hydrocarbon exploration using CSEM data. FIG. 5 shows synthetic (i.e., from model calculations) CSEM electric field amplitudes from two resistivity models in which the seawater is represented by an infinite half space above the seafloor. The solid line 52 corresponds to a model containing a reservoir at 2 km below the seafloor and the dashed line 54 corresponds to a model in which the reservoir is absent. The phases of the data are not shown. In these examples, the frequency and non-reservoir resistivities are such that the effect of the reservoir becomes apparent at offsets greater than about 4 km. Of course, actual data may be partially obscured by noise but, in any event, the CSEM data interpreter will rely on the distinction between the two curves to infer the presence or absence of a hydrocarbon reservoir. FIG. 5 represents an ideal or desired situation where the data are uncontaminated by air waves.
By contrast, FIG. 6 compares synthetic data with a reservoir present (solid line 62) and absent (dashed line 64). Here, the seawater is only 200 m thick beneath an infinite half-space of air. The synthetic data are markedly different from FIG. 5, being dominated by air-wave noise at offsets beyond about 5 km. The strong air wave is not surprising, since the water thickness is only about one-half of a skin depth at the 0.5 Hz frequency used for these computer simulations. The small difference between the curves in FIG. 6 with and without a reservoir present implies that the CSEM data interpreter may have a great deal of difficulty identifying the presence of a reservoir, particularly in the presence of other noises and normal resistivity variations that are not associated with hydrocarbons. FIG. 6 thus represents a common, but undesirable situation in which hydrocarbon signatures in CSEM data are obscured by air-wave noise. Clearly, it is desirable to have effective methods of removing air waves from CSEM data.
The problem of removing air-wave noise from marine CSEM data has only recently attracted attention as interest has heightened in using these surveys for oil and gas exploration. Two solutions are known in the published literature. In PCT application WO 03/100467A1, Amundsen discloses mathematical methods for resolving the electromagnetic wavefield recorded at the receivers into upgoing and downgoing components and then analyzing the upgoing component to derive the nature of the strata beneath the seafloor. Amundsen acknowledges that downward-traveling energy includes both energy propagating from the source to the receiver by way of the air-water boundary as well as energy propagating from the source to the subsea strata before propagating to the air-water boundary and to the receiver. As described above, such multiply-reflected signals are significantly imprinted by the electrical properties of air and most properly counted as air-wave noise. In PCT application WO 05/010560A1, Lu et al. disclose a method of subtracting from the air-wave contaminated data the difference between two synthetic data sets representing (1) the earth response beneath an infinite half-space of water and (2) the earth response beneath an infinite half-space of air and a water layer of finite thickness.
Both of these approaches must make various assumptions and approximations that can render them ineffective and costly. Amundsen must assume that upgoing energy is free of air-wave noise. In fact, upgoing energy includes some air-wave noise, as can be seen in FIG. 7 showing upgoing electromagnetic energy amidst layers of air 71, water 72, and earth 73. The upgoing (at the receiver) energy following path 74 from source location 10 to receiver 11 is preserved for analysis by Amundsen's method. However, energy following path 77 from source location 78 is also preserved for analysis even though it includes air-wave noise. Amundsen's formulae for removing downgoing energy require measurements of both the electric and magnetic fields at each receiver location. It is not always possible or economically practical to measure both the electric and magnetic field components with equal accuracy.
Lu et al. require that a resistivity model of the sub-sea sediments be developed. This model is then varied to generate the synthetic air-wave noise that is to be subtracted from the measured data. But the model is itself uncertain and must be determined from the data and any a priori information. Errors in this model will generate an erroneous estimate of the air-wave noise, leading to errors in the data following air-wave suppression.
Accordingly, an improved method is needed for correcting CSEM data for air wave effects. The present invention satisfies this need.